The local radio station is giving away some tickets to the circus. Adult tickets cost the station $8 each while children’s tickets cost $6. The station wants to spend no more than $172. Let x = the number of adult tickets and y = the number of children’s tickets. Show all possible solutions by graphing a linear inequality.
A.
B.
The local radio station is giving away some tickets to the circus. Adult tickets cost the station $8 each while children’s tickets cost $6. The station wants to spend no more than $172. Let x = the number of adult tickets and y = the number of children’s tickets. Show all possible solutions by graphing a linear inequality.
To graph the linear inequality for this problem, we need to set up the equation based on the given information.
The cost of adult tickets is $8 and the cost of children's tickets is $6. The station wants to spend no more than $172. So we can set up the equation:
8x + 6y ≤ 172
To graph this equation, we need to rewrite it in slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept. Let's rearrange the equation:
6y ≤ 172 - 8x
y ≤ (172 - 8x) / 6
Now we can plot the graph by drawing the line y = (172 - 8x) / 6. This line will represent the boundary of the feasible region. We can then shade the area below the line to represent the solutions to the inequality (since we want to spend no more than $172).
The graph will look like:
```
.............(5, 0)..............(0, 29).........................
...┌───────────────┐
...|<<<<<<<<<<<<<<|........................................................
...|<<<<<<<<<<<<<<|........................................................
...|<<<<<<<<<<<<<<|........................................................
...|<<<<<<<<<<<<<<|........................................................
...|<<<<<<<<<<<<<<|.......................Boundary Line: y ≤ (172 - 8x) / 6
...( 0, 48)..┌────┘
.......... (20,0)
```
The shaded region below the line represents all possible solutions for the number of adult and children's tickets that the radio station can buy within their budget of $172.
To show all possible solutions by graphing a linear inequality, we need to create an inequality based on the given information.
Let x be the number of adult tickets and y be the number of children's tickets.
The cost of x adult tickets is 8x, and the cost of y children's tickets is 6y.
The station wants to spend no more than $172, so we can set up the inequality:
8x + 6y ≤ 172
To graph this inequality, we can first rewrite it in slope-intercept form:
6y ≤ -8x + 172
Next, we graph the line y = -8x/6 + 172/6, or y = -4/3x + 86/3. This line represents the boundary of our solution.
Finally, we shade the region below the line to represent the possible solutions.
The graph will show all the possible combinations of adult and children's tickets that the radio station can buy while spending no more than $172.
Unfortunately, as an AI text-based program, I am unable to create or display a graph directly. I can only guide you through the process of creating the graph. You can use graphing software or draw the graph manually on a piece of graph paper to see all the possible solutions.